High-precision interference measurement constellation error evolution method based on high-order characteristics

Abstract

The invention discloses a high-precision interference measurement constellation error evolution method based on high-order characteristics, and belongs to the technical field of space. The implementation method comprises the following steps: setting orbit states of three spacecrafts under an inertial system, and setting an orbit dynamic model and an initial state of each spacecraft; selecting a characteristic direction of an initial orbit injection error of the spacecraft, establishing a high-order model of the characteristic direction, and establishing a high-order inverse model of the characteristic direction; setting an orbit error evolution semi-analytical expression initial value based on high-order characteristics; calculating an orbit error evolution semi-analytical expression based on high-order features; constructing orbit error evolution semi-analytical expressions of the three spacecrafts; constructing a configuration stability index model; establishing a high-precision interference measurement constellation error evolution model based on the characteristic direction; and giving an initial deviation, calculating a configuration stability index deviation at a given moment, and realizing high-precision interference measurement constellation error evolution analysis based on the calculated configuration stability index deviation at the given moment.

Description

Technical Field

[0001] The invention belongs to the field of space technology and relates to a method for evolving constellation configuration errors by spatial high-precision interferometry based on high-order characteristic directions. Background Art

[0002] Interferometry has been one of the important technologies in the field of precision measurement since the 19th century, and has been widely used in precision industrial production and processing as well as basic scientific measurement. In recent decades, with the development of space science applications, such as space gravitational wave detection, high-precision interstellar laser interferometry has received widespread attention.

[0003] High-precision intersatellite laser ranging uses interference between two or more laser beams between satellites, and obtains intersatellite distance change information by reading the phase information of the interference signal. This technology is based on high-precision satellite-borne laser frequency stabilization, precision phase measurement, weak light phase-locking technology, intersatellite laser pointing control and other technologies, and can achieve picometer-level intersatellite displacement measurement. It has important value and application prospects in research fields such as space science and technology and basic physics experiments. The existing space high-precision interferometric measurement constellations that have been proposed include the "Tai Chi" plan proposed by the Chinese Academy of Sciences, the "Tianqin Plan" proposed by the Tianqin Center of Sun Yat-sen University, and the "LISA Plan" proposed by the European Space Agency (ESA).

[0004] In the study of high-precision interferometry constellations in space, the range of interferometry is affected by the arm length between the measuring instruments. Compared with ground-based interferometry, by deploying interferometry spacecraft in space to form a high-precision interferometry constellation in space, the measurement range can be significantly improved and the measurement of low-frequency signals can be achieved.

[0005] The space high-precision interferometry constellation usually includes three spacecraft forming an approximate equilateral triangle, forming a detection configuration with three laser measurement arms. The space high-precision interferometry constellation requires that the spacecraft cannot be actively controlled during the mission implementation, because active control will affect the performance of interferometry and lead to erroneous measurements. At the same time, the space high-precision interferometry constellation has extremely high requirements for its configuration stability, requiring that the three spacecraft form an approximate equilateral triangle during a long mission. Although the nominal orbit of the space high-precision interferometry constellation usually meets the configuration stability requirements through optimized design, due to the influence of orbital deviation, the spacecraft in the space high-precision interferometry constellation will deviate from its pre-set nominal orbit, thereby destroying the configuration stability of the space high-precision interferometry constellation. Therefore, it is necessary to predict the error evolution of configuration stability in the mission design stage and analyze the impact of orbital error on configuration stability, so as to provide support for mission orbit design.

[0006] It is very important to study the evolution method of constellation configuration error by high-precision interferometry in space. The existing evolution method of constellation configuration error by high-precision interferometry in space has low calculation accuracy and large amount of calculation, which cannot meet the task requirements. Therefore, it is necessary to study the evolution method of constellation configuration error by high-precision interferometry in space with high-precision and fast calculation speed. Summary of the invention

[0007] In order to solve the problem of inaccurate prediction in the prior art, the main purpose of the present invention is to provide a high-precision interferometric measurement constellation error evolution method based on high-order features, to quickly and accurately calculate the error evolution of the spatial high-precision interferometric measurement constellation, to calculate the deviation of the configuration stability index at a given time, and to realize the deviation prediction of the configuration stability based on the calculated deviation of the configuration stability index at a given time. The present invention has the advantages of high accuracy and fast speed in predicting the evolution of the constellation error.

[0008] To achieve the above object, the technical solution adopted in the present invention is as follows:

[0009] The invention discloses a high-precision interferometric measurement constellation error evolution method based on high-order features, which sets the orbital states of three spacecraft in the spatial high-precision interferometric measurement constellation in the inertial system, sets the orbital dynamics model and initial state of each spacecraft in the high-precision interferometric measurement constellation; selects the characteristic direction of the initial orbit entry error of the spacecraft according to the initial state of the spacecraft, establishes a high-order model of the characteristic direction, and establishes a high-order inverse model of the characteristic direction; sets the initial value of the semi-analytical expression of orbital error evolution based on the high-order features according to the high-order inverse model of the characteristic direction; calculates the semi-analytical expression of orbital error evolution based on the high-order features; constructs the semi-analytical expression of orbital error evolution of the three spacecraft in the spatial high-precision interferometric measurement constellation; constructs the configuration stability index model of the spatial high-precision interferometric measurement constellation; establishes the high-precision interferometric measurement constellation error evolution model based on the characteristic direction; given the initial deviation, calculates the deviation of the configuration stability index at a given moment, further analyzes the configuration stability based on the calculated deviation of the configuration stability index at a given moment, and obtains the configuration stability analysis result. Based on the obtained deviation of the configuration stability and the configuration stability analysis result, the accuracy of mission orbit optimization and orbit reconstruction is improved. The present invention has the advantages of high calculation accuracy and fast calculation speed, can perform on-orbit calculations, improve the efficiency of implementing space high-precision interferometric measurement constellation tasks, and reduce interferometric measurement errors.

[0010] The present invention discloses a high-precision interferometric measurement constellation error evolution method based on high-order features, comprising the following steps:

[0011] Step 1: Set the orbital states of the three spacecraft in the high-precision interferometry constellation in the inertial system to x1(t) = [r1(t); v1(t)], x2(t) = [r2(t); v2(t)] and x3(t) = [r3(t); v3(t)], and set the orbital dynamics model f[x(t), t] and initial state x0 of each spacecraft in the high-precision interferometry constellation.

[0012] The orbital states of the three spacecraft in the high-precision interferometric measurement constellation in the inertial system are set to x1(t) = [r1(t); v1(t)], x2(t) = [r2(t); v2(t)] and x3(t) = [r3(t); v3(t)], where the subscripts 1, 2, and 3 represent spacecraft 1, spacecraft 2, and spacecraft 3. The initial state of the spacecraft at the initial time t0 is represented by x 1,0 =x1(t0),x 2,0 =x2(t0) and x 3,0 =x3(t0).

[0013] The orbital dynamics model f[x(t),t] and initial state x0 = [r0; v0] of each spacecraft in the high-precision interferometry constellation are set as follows:

[0014]

[0015] Where f(x, t) is the spacecraft dynamics model, x0 = [r0; v0] is the initial state, r0 is the initial position vector, and v0 is the initial velocity vector. In formula (1), for the sake of convenience, the subscripts 1, 2, and 3 used to represent spacecraft 1, spacecraft 2, and spacecraft 3 are removed.

[0016] Step 2: According to the initial state of the spacecraft x0 = [r0; v0], select the characteristic direction of the initial orbital error of the spacecraft and establish a high-order model of the characteristic direction And calculate its coefficient and According to the established high-order model of the feature direction, a high-order inverse model of the feature direction is established And calculate the corresponding coefficient and

[0017] According to the initial state of the spacecraft x0 = [r0; v0], the characteristic direction of the initial orbital error of the spacecraft is selected as the modulus of the position vector and the velocity vector:

[0018] y0=[||r0||,||v0||] T (2)

[0019] Where y0 represents the feature direction. The high-order model of the feature direction is further established as follows:

[0020]

[0021] in represents the i-th element of the feature direction y0, represents the k1th element of the initial state x0, represents the k2th element of the initial state x0, and the symbol δ represents the deviation. and is a tensor, defined as:

[0022]

[0023] The high-order inverse model of the feature direction is established using the inverse tensor method as follows:

[0024]

[0025] in for The inverse tensor of for The inverse tensor of .

[0026] Step 3: High-order inverse model of the characteristic direction established in step 2 And the corresponding coefficients and Setting the initial value of the semi-analytical expression of orbit error evolution based on high-order characteristics and

[0027] Based on the high-order inverse model of the characteristic direction established in step 2, the high-order inverse model And the corresponding coefficients and Setting the initial value of the semi-analytical expression of orbit error evolution based on high-order characteristics and

[0028]

[0029] Step 4: Based on the orbital dynamics model f[x(t),t] of the spacecraft in the high-precision interferometric measurement constellation set in step 1 and the initial state x0, the initial value of the semi-analytical expression of orbital error evolution based on high-order characteristics set in step 3 and Calculate the semi-analytical expression of orbit error evolution based on high-order characteristics and

[0030] According to the orbital dynamics model f[x(t),t] of the spacecraft in the high-precision interferometric measurement constellation set in step 1 and the initial state x0, the initial value of the semi-analytical expression of orbital error evolution based on high-order characteristics set in step 3 and The semi-analytical expression of orbit error evolution based on high-order characteristics is calculated by numerical integration. and The expression and The derivative of is:

[0031]

[0032] in:

[0033]

[0034] where f i [x(t),t] represents the i-th element of the orbital dynamics model f[x(t),t].

[0035] Step 5: Semi-analytical expression of orbit error evolution based on high-order features calculated in step 4 and A semi-analytical expression for the orbit error evolution of three spacecraft in a high-precision interferometry constellation is constructed.

[0036] Based on the semi-analytical expression of orbit error evolution based on high-order characteristics calculated in step 4 and The semi-analytical expression of the orbit error evolution of the three spacecraft in the high-precision interferometry constellation is as follows:

[0037]

[0038] in y 1,0 Represents the characteristic direction vector of the first spacecraft, y 2,0 Represents the characteristic direction vector of the second spacecraft, y 3,0 represents the characteristic direction vector of the third spacecraft, and is the coefficient, defined as:

[0039]

[0040] Step 6: According to the orbital states x1(t)=[r1(t);v1(t)], x2(t)=[r2(t);v2(t)] and x3(t)=[r3(t);v3(t)] of the three spacecraft in the space high-precision interferometry constellation set in step 1 in the inertial system, a configuration stability index model z(t)=h[X(t)] of the space high-precision interferometry constellation is constructed.

[0041] The configuration stability indexes considered include arm length l ij (t), breathing angle θ i (t) and arm length change rate The corresponding function expression is as follows:

[0042]

[0043] in

[0044] r ij (t) = r i (t)-r j (t) (18)

[0045] v ij (t) = v i (t)-v j (t) (19)

[0046] make Represents the description vector of the configuration stability index, let Representing the state vectors of the three spacecraft, there is the following nonlinear mapping relationship:

[0047]

[0048] Where z(t)=h[X(t)] represents the model of the configuration stability index.

[0049] Step 7: Based on the spatial high-precision interferometry constellation configuration stability index model z(t)=h[X(t)] constructed in step 6, and the and A high-precision interferometric measurement constellation error evolution model based on characteristic directions is established.

[0050] According to the configuration stability index model z(t)=h[X(t)] of the spatial high-precision interferometry constellation constructed in step 6, the error evolution model of the high-precision interferometry constellation based on the characteristic direction is established as follows:

[0051]

[0052] in:

[0053]

[0054] Step 8: Based on the high-precision interferometric measurement constellation error evolution model based on the characteristic direction established in step 7, the initial deviation is given, and the configuration stability index deviation at a given time is calculated. Further, based on the calculated configuration stability index deviation at a given time, that is, the deviation of the predicted configuration stability, the configuration stability is analyzed to obtain the configuration stability analysis result.

[0055] The method further includes step 9: based on the deviation of the configuration stability and the configuration stability analysis result obtained in step 8, improving the accuracy of mission orbit optimization and orbit reconstruction.

[0056] Beneficial effects:

[0057] 1. The present invention discloses a method for error evolution of a high-precision interferometric measurement constellation based on high-order features. The method sets the orbital states of three spacecraft in a spatial high-precision interferometric measurement constellation in an inertial system, sets the orbital dynamics model and initial state of each spacecraft in the high-precision interferometric measurement constellation; selects the characteristic direction of the initial orbit insertion error of the spacecraft according to the initial state of the spacecraft, establishes a high-order model of the characteristic direction, and establishes a high-order inverse model of the characteristic direction; sets the initial value of a semi-analytical expression of orbit error evolution based on high-order features according to the high-order inverse model of the characteristic direction; calculates a semi-analytical expression of orbit error evolution based on high-order features; adopts high-order characteristic directions to capture high-order information of the initial error and effectively improve calculation accuracy.

[0058] 2. The present invention discloses a high-precision interferometric measurement constellation error evolution method based on high-order characteristics. Numerical integration is required only when calculating the semi-analytical expression of orbit error evolution based on high-order characteristics. Therefore, only one numerical integration is required, which has the advantage of high computational efficiency.

[0059] 3. The present invention discloses a high-precision interferometric measurement constellation error evolution method based on high-order features, which adopts the modulus of the initial position and the velocity vector as the characteristic direction, and establishes a high-precision interferometric measurement constellation error evolution model based on the characteristic direction; the characteristic direction selection method is simple, and there is no need to perform a large amount of calculation to obtain the characteristic direction, which further improves the efficiency of high-precision interferometric measurement constellation error evolution prediction. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 It is a flow chart of a method for high-precision interferometric measurement of constellation error evolution based on high-order features in the present invention. DETAILED DESCRIPTION

[0061] The embodiments of the present invention will be described in detail below in conjunction with the accompanying drawings, but those skilled in the art will understand that the following examples are only used to illustrate the present invention and should not be regarded as limiting the scope of the present invention.

[0062] Reference Figure 1 This embodiment discloses a high-precision interferometric measurement constellation error evolution method based on high-order features, and the specific implementation steps are as follows:

[0063] Step 1: Set the orbital states of the three spacecraft in the high-precision interferometry constellation in the inertial system to x1(t) = [r1(t); v1(t)], x2(t) = [r2(t); v2(t)] and x3(t) = [r3(t); v3(t)], and set the orbital dynamics model f[x(t), t] and initial state x0 of the spacecraft in the high-precision interferometry constellation.

[0064] The orbital states of the three spacecraft in the high-precision interferometric measurement constellation in the inertial system are set to x1(t) = [r1(t); v1(t)], x2(t) = [r2(t); v2(t)] and x3(t) = [r3(t); v3(t)], where the subscripts 1, 2, and 3 represent spacecraft 1, spacecraft 2, and spacecraft 3. The initial state of the spacecraft at the initial time t0 is represented by x 1,0 =x1(t0),x 2,0 =x2(t0) and x 3,0 =x3(t0), the initial state of the spacecraft at the initial time t0 is shown in Table 1.

[0065] Table 1 Initial state of the spacecraft at the initial time (initial time January 1, 2015)

[0066]

[0067] The orbital dynamics model f[x(t),t] and initial state x0=[r0;v0] of the spacecraft in the high-precision interferometry constellation are set as follows:

[0068]

[0069] Where f(x, t) is the spacecraft dynamics model, x0 = [r0; v0] is the initial state, r0 is the initial position vector, and v0 is the initial velocity vector. In formula (1), for the sake of convenience, the subscripts 1, 2, and 3 used to represent spacecraft 1, spacecraft 2, and spacecraft 3 are removed. The spacecraft dynamics model mainly includes the gravity of the sun's center and the perturbation force of the earth's third body. The specific dynamics model expression is:

[0070]

[0071] where μ s With μ e are the gravitational constants of the sun and the earth, r eis the position of the Earth in the heliocentric inertial system. The ephemeris used is DE432.

[0072] Step 2: According to the initial state of the spacecraft x0 = [r0; v0], select the characteristic direction of the initial orbital error of the spacecraft and establish a high-order model of the characteristic direction and According to the established high-order model of the feature direction, a high-order inverse model of the feature direction is established and

[0073] Step 3: High-order inverse model of the feature direction established in step 2 and Setting the initial value of the semi-analytical expression of orbit error evolution based on high-order characteristics and

[0074] Step 4: Based on the orbital dynamics model f[x(t),t] of the spacecraft in the high-precision interferometric measurement constellation set in step 1 and the initial state x0, the initial value of the semi-analytical expression of orbital error evolution based on high-order characteristics set in step 3 and Calculate the semi-analytical expression of orbit error evolution based on high-order characteristics and

[0075] Step 5: Semi-analytical expression of orbit error evolution based on high-order features calculated in step 4 and A semi-analytical expression for the orbit error evolution of three spacecraft in a high-precision interferometry constellation is constructed.

[0076] Step 6: According to the orbital states x1(t)=[r1(t);v1(t)], x2(t)=[r2(t);v2(t)] and x3(t)=[r3(t);v3(t)] of the three spacecraft in the space high-precision interferometry constellation set in step 1 in the inertial system, a configuration stability index model z(t)=h[X(t)] of the space high-precision interferometry constellation is constructed.

[0077] Step 7: Based on the configuration stability index model z(t)=h[X(t)] of the spatial high-precision interferometry constellation constructed in step 6, a high-precision interferometry constellation error evolution model based on the characteristic direction is established.

[0078] Step 8: Based on the high-precision interferometric measurement constellation error evolution model based on the characteristic direction established in step 7, given the initial deviation, calculate the configuration stability index deviation at a given time, and further analyze the configuration stability based on the calculated configuration stability index deviation at a given time to provide support for mission orbit optimization and orbit reconstruction.

[0079] The initial errors are set to: 100 km for single-axis position and 1 m / s for single-axis speed. The average relative error of the stability index predicted ten years later is 0.0851%, and the calculation time is only 21.5070 seconds, which illustrates the advantages in accuracy and efficiency of the high-precision interferometric measurement constellation error evolution method based on high-order features disclosed in the present invention.

[0080] The specific description above further illustrates in detail the purpose, technical solutions and beneficial effects of the invention. It should be understood that the above is only a specific embodiment of the present invention, which is used to explain the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A high-precision interferometric measurement constellation error evolution method based on high-order features, characterized by: The following steps are included: Step 1: Set the orbital states of the three spacecraft in the high-precision interferometry constellation in the inertial system to x1(t) = [r1(t); v1(t)], x2(t) = [r2(t); v2(t)] and x3(t) = [r3(t); v3(t)], and set the orbital dynamics model f[x(t), t] and initial state x0 of each spacecraft in the high-precision interferometry constellation; Step 2: According to the initial state of the spacecraft x0 = [r0; v0], select the characteristic direction of the initial orbital error of the spacecraft and establish a high-order model of the characteristic direction And calculate its coefficient and According to the established high-order model of the feature direction, a high-order inverse model of the feature direction is established And calculate the corresponding coefficient and Step 3: High-order inverse model of the characteristic direction established in step 2 And the corresponding coefficients and Setting the initial value of the semi-analytical expression of orbit error evolution based on high-order characteristics and Step 4: Based on the orbital dynamics model f[x(t),t] of the spacecraft in the high-precision interferometric measurement constellation set in step 1 and the initial state x0, the initial value of the semi-analytical expression of orbital error evolution based on high-order characteristics set in step 3 and Calculate the semi-analytical expression of orbit error evolution based on high-order characteristics and Step 5: Semi-analytical expression of orbit error evolution based on high-order features calculated in step 4 and Construct a semi-analytical expression for the orbit error evolution of three spacecraft in a high-precision interferometry constellation; Step 6: According to the orbital states x1(t)=[r1(t);v1(t)], x2(t)=[r2(t);v2(t)] and x3(t)=[r3(t);v3(t)] of the three spacecraft in the space high-precision interferometry constellation set in step 1, a configuration stability index model z(t)=h[X(t)] of the space high-precision interferometry constellation is constructed; Step 7: Based on the spatial high-precision interferometry constellation configuration stability index model z(t)=h[X(t)] constructed in step 6, and the and Establish a high-precision interferometric constellation error evolution model based on characteristic directions; Step 8: Based on the high-precision interferometric measurement constellation error evolution model based on the characteristic direction established in step 7, the initial deviation is given, and the configuration stability index deviation at a given time is calculated. Further, based on the calculated configuration stability index deviation at a given time, that is, the deviation of the predicted configuration stability, the configuration stability is analyzed to obtain the configuration stability analysis result.

2. The high-precision interferometric measurement constellation error evolution method based on high-order features as claimed in claim 1, characterized in that: Step 1 is implemented as follows: The orbital states of the three spacecraft in the high-precision interferometric measurement constellation in the inertial system are assumed to be x1(t) = [r1(t); v1(t)], x2(t) = [r2(t); v2(t)] and x3(t) = [r3(t); v3(t)], where the subscripts 1, 2, and 3 represent spacecraft 1, spacecraft 2, and spacecraft 3; the initial state of the spacecraft at the initial time t0 is represented by x 1,0 =x1(t0),x 2,0 =x2(t0) and x 3,0 =x3(t0); The orbital dynamics model f[x(t),t] and initial state x0 = [r0; v0] of each spacecraft in the high-precision interferometry constellation are set as follows: Where f(x, t) is the spacecraft dynamics model, x0 = [r0; v0] is the initial state, r0 is the initial position vector, and v0 is the initial velocity vector. In formula (1), the subscripts 1, 2, and 3 used to represent spacecraft 1, spacecraft 2, and spacecraft 3 are removed.

3. The high-precision interferometric measurement constellation error evolution method based on high-order features as claimed in claim 2, characterized in that: Step 2 is implemented as follows: According to the initial state of the spacecraft x0 = [r0; v0], the characteristic direction of the initial orbital error of the spacecraft is selected as the modulus of the position vector and the velocity vector: y0=[||r0||,||v0||] T (2) Where y0 represents the feature direction; the high-order model of the feature direction is further established as follows: in represents the i-th element of the feature direction y0, represents the k1th element of the initial state x0, represents the k2th element of the initial state x0, and the symbol δ represents the deviation. and is a tensor defined as: The high-order inverse model of the feature direction is established using the inverse tensor method as follows: in for The inverse tensor of for The inverse tensor of .

4. The high-precision interferometric measurement constellation error evolution method based on high-order features as claimed in claim 3, characterized in that: Step 3 is implemented as follows: Based on the high-order inverse model of the characteristic direction established in step 2, the high-order inverse model And the corresponding coefficients and Setting the initial value of the semi-analytical expression of orbit error evolution based on high-order characteristics and 。 5. The high-precision interferometric measurement constellation error evolution method based on high-order features as claimed in claim 4, characterized in that: Step 4 is implemented as follows: According to the orbital dynamics model f[x(t),t] of the spacecraft in the high-precision interferometric measurement constellation set in step 1 and the initial state x0, the initial value of the semi-analytical expression of orbit error evolution based on high-order characteristics set in step 3 and The semi-analytical expression of orbit error evolution based on high-order characteristics is calculated by numerical integration. and The expression and The derivative of is: in: where f i [x(t),t] represents the i-th element of the orbital dynamics model f[x(t),t].

6. The high-precision interferometric measurement constellation error evolution method based on high-order features as claimed in claim 5, characterized in that: Step 5 is implemented as follows: Based on the semi-analytical expression of orbit error evolution based on high-order characteristics calculated in step 4 and The semi-analytical expression of the orbit error evolution of the three spacecraft in the high-precision interferometry constellation is as follows: in y 1,0 Represents the characteristic direction vector of the first spacecraft, y 2,0 Represents the characteristic direction vector of the second spacecraft, y 3,0 represents the characteristic direction vector of the third spacecraft, and is the coefficient, defined as: 。 7. The high-precision interferometric measurement constellation error evolution method based on high-order features as claimed in claim 6, characterized in that: In step 6, The configuration stability indicators considered include arm length l ij (t), breathing angle θ i (t) and arm length change rate l ij (t), the corresponding function expression is as follows: in r ij (t)=r i (t)-r j (t) (18) v ij (t)=v i (t)-v j (t) (19) make Represents the description vector of the configuration stability index, let Representing the state vectors of the three spacecraft, there is the following nonlinear mapping relationship: Where z(t)=h[X(t)] represents the model of the configuration stability index.

8. The high-precision interferometric measurement constellation error evolution method based on high-order features as claimed in claim 7, characterized in that: Step 7 is implemented as follows: According to the configuration stability index model z(t)=h[X(t)] of the spatial high-precision interferometry constellation constructed in step 6, the error evolution model of the high-precision interferometry constellation based on the characteristic direction is established as follows: in: 。

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